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Bjoerck A., Dahlquist G. — Numerical mathematics and scientific computation
Bjoerck A., Dahlquist G. — Numerical mathematics and scientific computation

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Название: Numerical mathematics and scientific computation

Авторы: Bjoerck A., Dahlquist G.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 673

Добавлена в каталог: 19.11.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
A-norm      333
A-orthogonal vectors      336
Adjoint matrix      190
Aitken extrapolation      237
Algorithm, $LDL^{T}$      29
Algorithm, back-substitution      6
Algorithm, back-substitution, banded      25
Algorithm, band LU      24
Algorithm, band-Cholesky      36
Algorithm, block Cholesky      48
Algorithm, block LU factorization      47
Algorithm, block-Cholesky factorization      48
Algorithm, CG      340
Algorithm, CGLS      351
Algorithm, CGNE      351
Algorithm, CGNR      365
Algorithm, Cholesky factorization      34
Algorithm, classical Gram — Schmidt      121
Algorithm, compact LU      19
Algorithm, Euler — Newton method      399
Algorithm, forward-substitution, banded      25
Algorithm, Gaussian elimination      7
Algorithm, Givens rotations      132 247
Algorithm, Householder QR      136
Algorithm, Householder reflection      131
Algorithm, incomplete Cholesky      372
Algorithm, incomplete LU      369
Algorithm, IRLS      183
Algorithm, Lanczos      285 359
Algorithm, MGS, least squares by      126
Algorithm, MGS, minimum norm solution by      127
Algorithm, modified Gram — Schmidt      123
Algorithm, orthogonal iteration      281
Algorithm, preconditioned CG      363
Algorithm, preconditioned CGNE      365
Algorithm, Rayleigh — Ritz procedure      279
Algorithm, recursive Cholesky factorization      51
Algorithm, svd      230 234
Algorithm, The Arnoldi process      288
Algorithm, tridiagonal spectrum slicing      254
Algorithm, Vandermonde system      85
Algorithm, Vandermonde system, dual      84
Analytic function of matrix      207
Armijo — Goldstein criterion      396
Arnoldi's method      288—289 354—358
Arnoldi's process      355
Arrowhead matrix      253
Augmented linear system      96
Augmented system      140—141
B-splines, cubic      142
Back-substitution      5
Back-substitution, banded      25
Banach space      387
Banded matrix of standard form      141
Banded systems      23—36
Bandwidth of LU factors      23
Bandwidth, lower      23
Bandwidth, row      101
Bandwidth, upper      23
Bauer — Fike's theorem      217
BCG      see "Bi-conjugate gradient"
BFGS update      406
Bi-conjugate gradient method      360
Bidiagonal decomposition, Lanczos process      287
Bidiagonal form, reduction to      153—155
Bidiagonal matrix      23
Bilinear      442
Bordered matrix      54
Broyden's method      393
Canonical form, Kronecker      291
Canonical form, Schur      199—202
Cauchy matrix      87
Cayley — Hamilton theorem      204
CG      see also "Conjugate gradient"
CG method, preconditioned      363—364
cgs      361 see
Characteristic equation      191
Characteristic polynomial      191
Chebyshev polynomials      328
Chebyshev semi-iterative method      330
Cholesky factorization      33—37 100
Cholesky factorization, backward error      74
Cholesky factorization, block incomplete      373
Cholesky factorization, incomplete      371
Cholesky factorization, sparse      62
Cholesky factorization, symbolic      62
Column scaling      117
Column scaling, optimal      105
Condition estimation      71—72 157—158
Condition estimation, Hager's      72
Condition number of matrix      65
Condition number, general matrix      115
Conjugate gradient method      338—344
Conjugate gradient method, preconditioned      364—366
Conjugate gradient method, rate of convergence      342
Conjugate residual method      341 345
Consistently ordered      320
Constrained problem, quadratic inequality      172—175
Continuation method      398—399
Contraction      386
Contraction mapping theorem      386
Convergence, acceleration of      327—331
Convergence, asymptotic rate      311
Convergence, average rate      311
Convergence, conditions for      309
Convergent matrix      309
Convex set      427
Cost vector      427
Covariance matrix      92—94 102
Covariance matrix, estimate      101
Covariance matrix, method      161
Craig's method      351
Cramer's rule      2
Crout's algorithm      19
CS decomposition      295—296
Decomposition, block diagonal      202
Decomposition, CS      295—296
Decomposition, GSVD      296
Decomposition, SVD      108
Defect matrix      374
Deflation      238—239
Deflation of matrix      195 239
Degeneracy      434—436
Departure from normality      202
Derivative, directional      444
Derivative, Frechet      444
Derivative, Gateaux      444
Derivative, higher, vector-valued      444
Derivative, partial      444
Descent direction      395 403
Diagonal scaling, optimal      368
Differentials, elementary      447
Direct elimination, method of      170
Direct methods, fast      374—376
Directional derivative      444
Distance to singular matrices      67
Divide and conquer, tridiagonal eigenproblem      252—253
Dominant, invariant subspace      244
Doolittle's algorithm      19
Double pendulum      401
Downdating, Cholesky factorization      168
Downdating, Gram — Schmidt decomposition      167—168
Downdating, QR decomposition      166—167
Downdating, Saunders algorithm      170
Eigenvalue by spectrum slicing      254—256
Eigenvalue of Kronecker product      197
Eigenvalue of Kronecker sum      197
Eigenvalue of matrix      191
Eigenvalue problem, large      278—289
Eigenvalue, algebraic multiplicity      195
Eigenvalue, defective      196
Eigenvalue, dominant      237
Eigenvalue, error bound      223—226
Eigenvalue, geometric multiplicity      195
Eigenvalue, Jacobi's method      229—232
Eigenvalue, perturbation      217—226
Eigenvalue, power method      236—245
Eigenvalue, subspace iteration      243—245
Eigenvector of matrix      191
Eigenvector, perturbation      217—226
Element growth      10 27 73
Element growth, Bunch — Kaufman pivoting      39
Element growth, complete pivoting      74
Element growth, partial pivoting      74
Elementary differentials      447 450
Elementary reflector      130
Elementary rotations, unitary      236
Elliptic equation      344
Envelope of LU factors      56
Envelope of matrix      56
Error bounds, a posteriori      70
Error bounds, backward      69
Error, componentwise estimate      158
Errors-in-variable model      178
Euler expansion      377
Exchange matrix      22
Expansion, Euler      377
Expansion, Neumann      377
Exponential fitting      408
Exponential of matrix      206
Fast Fourier Transform      375
Feasible point      384
Feasible point, basic      430
Feasible point, degenerate      430
Feasible region      384
Field of values      224
Fill-in      55
Filter factor      146
Fischer's theorem      111 221
Fixed Point Iteration      385—388
FLOP      7
Flop count, $LDL^{T}$      30
Flop count, banded back-substitution      25
Flop count, banded LU      25
Flop count, Cholesky factorization      100
Flop count, condition estimation      72
Flop count, Gauss — Jordan elimination      18
Flop count, Gaussian elimination      8
Flop count, Gram — Schmidt      123
Flop count, Hessenberg system      25
Flop count, Householder QR      144
Flop count, inverse matrix      21
Flop count, normal equations      100
Flop count, QR algorithm for SVD      274
Flop count, QR factorization      137 158
Flop count, QR factorization, banded      141
Flop count, QR step      262
Flop count, reduction to bidiagonal form      154
Flop count, reduction to Hessenberg form      249 250
Flop count, triangular system      8
Flop count, tridiagonal system      26
Forward-substitution, banded      25
Frechet derivative      443
Functional equation      383
Functions, matrix-valued      206—212
Fundamental subspaces      114
Gap of spectrum      279
Gateaux derivative      444
Gauss — Jordan elimination      18
Gauss — Markoff 's theorem      93
Gauss — Newton method      409—413
Gauss — Newton method, rate of convergence      413
Gauss — Seidel's method      304 335
Gauss — Seidel's method, nonlinear      385
Gaussian elimination      3—20
Gaussian elimination, backward error      73
Gaussian elimination, block algorithms      46—53
Gaussian elimination, compact schemes      18—20
Gaussian elimination, matrix representation of      15
Gaussian elimination, rounding error analysis      73—76
Gaussian elimination, scaling invariance      77
ge      see "Gaussian elimination"
Generalized eigenvalue problem      290—294
Generalized SVD      296—297
Geometric fitting      420
Gershgorin disks      215
Gershgorin's theorem      215 216
Givens rotation      131
Givens rotation, unitary      247
GKBD      see "Golub — Kahan bidiagonalization"
Global convergence      395—397
gmres      354—358
GMRES, preconditioned      366
GMRES, restarted      358
Golub — Kahan bidiagonalization      287—288 352
Golub — Kahan bidiagonalization in finite precision      288
Grade of vector      196
Graded matrix      251
Gradient vector      387 402
Gram — Schmidt decomposition, downdating of      167—168
Gram — Schmidt decomposition, modifying      167—168
Gram — Schmidt, classical      121
Gram — Schmidt, modified      123
Gram — Schmidt, orthogonalization      121—129
Graph, connected      193
Graph, directed      193
Graph, ordered      59
Graph, undirected      59
Growth ratio      10 73 250
Hankel matrix      86
Hermitian matrix      190
Hessenberg form, reduction to      248—250
Hessenberg matrix      23
Hessenberg matrix, unreduced      198 263
Hessian matrix      402 445
Hestenes method      233—234
Hilbert matrix      87
Homotopy      398
Hotelling      239
Householder reflection, unitary      247
Householder reflector      130
Hyperbolic rotations      133
ill-posed problems      172—175
Implicit function      443
Incomplete factorization      369—374
Incomplete factorization, block      372—374
Incomplete factorization, Cholesky      371
Incomplete factorization, LU      369
Incremental loading      399
Inertia of matrix      223
Initial basis      437
Inner iteration      373
Instability, irrelevant      249
Invariant subspace      193
Inverse function      443
Inverse iteration      239—242
Inverse iteration, shift      240
Inverse of band matrix      26
Inverse, left      121
Inverse, product form of      18
IRLS      see "Iteratively reweighted least squares"
Iteration matrix      308
Iteration matrix, Gauss — Seidel      309
Iteration matrix, Jacobi      309
Iteration matrix, SOR      319
Iteration matrix, SSOR      324
Iterative method, block      325—326
Iterative method, classical      348
Iterative method, convergent      309
Iterative method, error reducing      350
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